CBSE Class 9 Science — Work and Energy

Chapter Overview & Weightage

Work and Energy is one of the most practical and conceptually important chapters in Class 9 Science. It bridges everyday observations (why does a ball slow down? where does energy go?) with mathematical rigour. In CBSE SA exams, this chapter carries 6–10 marks consistently.

Year	Marks	Question Types
2023	8	2 MCQ + 1 short + 1 numerical
2022	10	1 MCQ + 2 short + 1 long
2021	6	1 MCQ + 1 short + 1 numerical
2020	8	2 short + 1 long

Numericals on kinetic energy, potential energy, and work-energy theorem appear in almost every CBSE SA exam. The law of conservation of energy — especially for a falling body — is a must-know long answer.

Key Concepts You Must Know

Work — In physics, work is done only when a force causes displacement in the direction of the force.

W = F \cdot d \cdot \cos\theta

Work is zero when: (1) force is zero, (2) displacement is zero, or (3) force is perpendicular to displacement ( $\theta = 90°$ ).

Energy — the capacity to do work. SI unit: Joule (J). 1 J = 1 N·m = 1 kg·m²/s²

Power — the rate of doing work: $P = W/t$ . SI unit: Watt (W). 1 W = 1 J/s. Also: 1 horsepower = 746 W.

Kinetic Energy (KE):

KE = \frac{1}{2}mv^2

Potential Energy (PE): Energy stored due to position or configuration.

PE = mgh \quad \text{(gravitational potential energy)}

Law of Conservation of Energy: Energy can neither be created nor destroyed — it can only be converted from one form to another. Total mechanical energy (KE + PE) remains constant in the absence of friction.

Important Formulas

W = Fd\cos\theta

KE = \frac{1}{2}mv^2

PE = mgh

\text{Work-Energy Theorem: } W_{net} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2

P = \frac{W}{t} = Fv

Deriving KE from work done:

Consider a body of mass $m$ starting from rest, accelerated by force $F$ over displacement $s$ :

Using $v^2 = u^2 + 2as$ with $u = 0$ : $v^2 = 2as$ , so $a = v^2/2s$

Work done = $F \cdot s = ma \cdot s = m \cdot \frac{v^2}{2s} \cdot s = \frac{1}{2}mv^2$

This derivation is asked in CBSE 5-mark questions.

Solved Previous Year Questions

PYQ 1 — 2023 CBSE

Q: A body of mass 5 kg is moving with velocity 4 m/s. Calculate its kinetic energy.

KE = \frac{1}{2}mv^2 = \frac{1}{2} \times 5 \times (4)^2 = \frac{1}{2} \times 5 \times 16 = 40 \text{ J}

Answer: KE = 40 J

PYQ 2 — 2022 CBSE

Q: A ball of mass 0.5 kg is thrown upward with velocity 20 m/s. Find its KE and PE at the highest point. (g = 10 m/s²)

At the highest point, velocity = 0.

KE = \frac{1}{2} \times 0.5 \times 0^2 = 0 \text{ J}

Height reached: $h = \frac{v^2}{2g} = \frac{(20)^2}{2 \times 10} = 20$ m

PE = mgh = 0.5 \times 10 \times 20 = 100 \text{ J}

Total energy = 100 J (all converted to PE). Initial KE = $\frac{1}{2}(0.5)(20)^2 = 100$ J. ✓ Energy is conserved.

PYQ 3 — 2021 CBSE

Q: Show that when a body falls freely, the total mechanical energy remains constant.

Consider a body of mass $m$ at height $H$ , falling freely. At three positions:

At top (before falling): $v = 0$

$KE = 0$
$PE = mgH$
Total $E = mgH$

At midpoint (height $H/2$ ): Using $v^2 = 2g(H/2) = gH$

$KE = \frac{1}{2}mv^2 = \frac{1}{2}m(gH) = \frac{mgH}{2}$
$PE = mg(H/2) = \frac{mgH}{2}$
Total $E = mgH$ ✓

At ground (height 0): Using $v^2 = 2gH$

$KE = \frac{1}{2}m(2gH) = mgH$
$PE = 0$
Total $E = mgH$ ✓

Total energy is $mgH$ at all three positions — energy is conserved.

Difficulty Distribution

Difficulty	%	Type of Questions
Easy	35%	KE/PE calculations, units, definitions
Medium	50%	Work-energy theorem, energy conservation numericals
Hard	15%	Multi-step problems, derivations

Expert Strategy

Always check units. Many students get the formula right but lose marks due to inconsistent units. If mass is in kg and velocity in m/s, energy comes out in Joules automatically — no conversion needed.

The falling body conservation problem is a guaranteed 5-mark question. Practise showing that KE + PE = constant at three points (top, middle, bottom).

When asked “find work done by a force at 60° to displacement,” don’t forget to multiply by $\cos 60° = 0.5$ . Students often apply $W = Fd$ directly and lose half the marks.

Power questions at Class 9 level usually involve simple $P = W/t$ or $P = Fv$ . If a machine lifts mass $m$ through height $h$ in time $t$ : $P = mgh/t$ .

Common Traps

Trap 1: “No work is done when you carry a heavy bag while walking horizontally.” This trips students. The carrying force is vertical (upward), the displacement is horizontal — they are perpendicular. $\cos 90° = 0$ , so $W = 0$ . CBSE loves this conceptual question.

Trap 2: Confusing work done by a force vs work done against a force. Work done against gravity = $+mgh$ (positive, you’re storing PE). Work done by gravity when falling = $+mgh$ (gravity does positive work as object moves in direction of gravity). Read the question carefully.

Trap 3: Commercial unit of energy is kWh (kilowatt-hour), not kW or Wh alone. 1 kWh = $3.6 \times 10^6$ J. This conversion appears in electricity bill problems.